A369894 a(n) = n * Sum_{p|n, p prime} tau(n/p) / p.

0, 1, 1, 4, 1, 10, 1, 12, 6, 14, 1, 36, 1, 18, 16, 32, 1, 51, 1, 52, 20, 26, 1, 104, 10, 30, 27, 68, 1, 124, 1, 80, 28, 38, 24, 180, 1, 42, 32, 152, 1, 164, 1, 100, 87, 50, 1, 272, 14, 115, 40, 116, 1, 216, 32, 200, 44, 62, 1, 432, 1, 66, 111, 192, 36, 244, 1, 148

Offset: 1

Author

Wesley Ivan Hurt, Feb 04 2024

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000005 (tau), A062799, A319131, A369893.

Programs

Mathematica

Table[n*DivisorSum[n, DivisorSigma[0, n/#]/# &, PrimeQ[#] &], {n, 80}]

PARI

A369894(n) = if(1==n, 0, my(f=factor(n)); n*sum(i=1, #f~, (numdiv(n/f[i, 1])/f[i,1]))); \\ Antti Karttunen, Jan 22 2025

Formula

a(p^k) = k*p^(k-1), for prime p and k >= 1. - Wesley Ivan Hurt, Jun 26 2024